G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395 (2013)
385
Introduction
Genetically engineered enzymes of modified structure are proved
very effective biocatalysts for many biosyntheses of industrial
interest, which tend more and more to replace some of the classical
fine chemical synthesis processes. Engineered enzymat- ic
reactions, displaying a high selectivity and speci- ficity, are
sustainable bioengineering routes to ob- tain a wide range of
biochemical products in food, pharmaceutical, detergent, textile
industry, bio-re- newable energy industries, or present challenging
applications in medicine.1,2 Biocatalytic processes produce fewer
by-products, consume less energy, and generate less environmental
pollution, require smaller catalyst concentrations and moderate
reac- tion conditions. However, the crucial aspect in any realistic
engineering analysis for process design, operation, control, and
optimization relies on the knowledge of an adequate and
sufficiently reliable mathematical model. Such a model, preferably
based on the process mechanism and developed at
various detailing levels (enzyme, reaction, reactor, process,
separately identified and linked using spe- cific methodologies),
has to ensure interpretable and reliable predictions of the process
behaviour under varied operating conditions.2–4
In particular, special attention was paid over the decades to
aldose reductase (EC 1.1.1.21, alde- hyde reductase), being
justified by its medical ap- plications: involvement of ALR in the
glucose me- tabolism (glucose conversion to sorbitol, galactose
reduction to galactitol), development of diabetic cataract (leading
to eye and nerve damage due to sorbitol overproduction),5 of the
myocardial isch- emic injury,6 and other putative physiological
pro- cesses related to steroid and catecholamine metabo- lism.7 As
a member of the aldo-keto reductase superfamily,7 the ALR catalyzes
the NADPH-de- pendent unspecific reduction of a wide variety of
carbonyl-containing aliphatic and aromatic com- pounds to their
corresponding alcohols, and espe- cially of aldoses, and
corticosteroids (although the enzyme can also utilize the cheaper
NADH in- stead).8,9 For such reasons, ALR has high potential for
industrial applications, e.g. for the production of
Modelling Enzymatic Reduction of 2-keto-D-glucose by Suspended
Aldose Reductase
G. Mariaa,* and M. D. Enea,b
aUniversity Politehnica of Bucharest, Department of Chemical &
Biochemical Engineering, Polizu Str. 1, 011061 Bucharest, P.O.
35-107, Romania bBiotehnos Co. s.a., R&D Department, Gorunului
Str. 3-5, 075100 Otopeni, Romania
Batch experiments have been systematically carried out at 25 °C, pH
= 7, over 24-76 h reaction time in order to evaluate the activity
of a commercial (recombinant human) aldose reductase (ALR) used to
catalyze the reduction of 2-keto-D-glucose (kDG) to fructose using
NADPH as cofactor, by employing various enzyme/reactants initial
ratios. A kinetic model was proposed by extending the ‘core’
reaction mechanism proposed in literature for the reduction of
several saccharides and keto-derivates (glu- cose, galactose,
xylose, glyceraldehydes) by the human or animal ALR (wild or modi-
fied), or by similar aldo-keto reductases (e.g. sorbitol
dehydrogenase, xylose reductase) in the presence of NAD(P)H. The
reaction pathway assumes a very quick reversible formation of a
stable ALR•NADPH complex, from which a small fraction is binding
the substrate thus determining a succession of Bi-Bi reversible
reactions leading to the final product (fructose). Model parameters
have been estimated based on the recorded data sets of four
observable key-species, being in concordance with the reported
values in literature for similar processes. The results confirm the
conformational change of E•NADP+ complex allowing the release of
NADP+ as being the rate-limiting step of the overall process. The
results also underline the necessity to stabilize the fast
deactivating enzyme by immobilization, as well as the requirement
of a continuous in-situ regenera- tion of the cofactor.
Key words: Keto-glucose reduction to fructose, aldose reductase,
reaction mechanism, kinetic model
*Corresponding author: Tel: +40 744 830308, E-mail:
[email protected]
Original scientific paper Received: February 14, 2013
Accepted: March 26, 2013
386 G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395
(2013)
polyols largely used as sweeteners (e.g. sorbitol, mannitol,
xylitol, erythritol),10 for the production of chiral
hydroxy-beta-lactams,11 of arabitol, or of rib- itol.12 ALR can
also be used for glucose transforma- tion to fructose, either by
glucose reduction to sor- bitol followed by its oxidation to
fructose (catalyzed by sorbitol dehydrogenase),13 or by oxidation
of glucose to keto-glucose followed by the reduction of the latter
to fructose (Cetus process).14
ALR is a small monomeric protein, with a mo- lecular mass of 34–43
kDa depending on the en- zyme source, present in most of animal
cells (liver, kidney, lens, retina, muscles, peripheral nerves, red
blood cells, etc.).15 The commercially purified re- combinant ALR,
including 315 aminoacid residues, is produced by expressing the
human ALR in E. coli. Even if presenting multiple forms,7,16–18 the
basic ALR structure consists of a β/α-”barrel” motif made up of
eight parallel β strands, the adjacent strands being connected by
eight peripheral α-helical segments. The larger active hydrophobic
catalytic site is situated in the barrel core, where the cofactor
NADPH binds in an extended conformation. The catalytic carbon C4 of
the nicotinamide ring of NADP+ is located at the bottom of a deep
cleft and having the pyrophosphate straddling the barrel lip.7,9,19
Aminoacid residues Asp-43, Tyr-48, Lys- 77, His-110, Asn-160, and
Gln-183, highly con- served in all aldo-ketoreductases, form a
tight net- work of hydrogen bonds linked to the nicotinamide ring
(see 3D plots of human ALR given by Blakeley et al.9). The tertiary
enzyme structure retains con- siderable flexibility, and many
compounds with dif- ferent chemical structures (inhibitors,
activators) can interact with the enzyme in different conforma-
tions.
Although ALR is active with both NADPH and NADH coenzymes, the
enzyme prefers NADP(H) approximately 2-fold to NAD(H) (in terms of
reac- tion rate), due to better apparent binding of the
phosphorylated form of the coenzyme.20,21 In spite of its higher
instability and much higher cost vs. NADH, the NADPH remains the
main co-enzyme in ALR catalyzed reactions, with multiple possibili-
ties to be regenerated by means of redox reactions conducted
in-situ or in separate regenerative sys- tems.22 Chemical
modification of ALR with pyri- doxal 5’-phosphate could avoid the
oxidation-in- duced activation, thus increasing its
activity.20
Optimal ALR activity is reported for tempera- tures of 25–50 °C and
pH = 5.8–10 depending on the substrate used.23 For instance, an
optimum of {50 °C, pH = 6} was found for D-xylose enzymat- ic
reduction with NADH,20 of {25 °C, pH = 8} for its reduction with
NADPH,24 of {25 °C, pH = 7} for glycolaldehyde reduction,17 or of
{20–37 °C, pH = 6–7} for DL-glyceraldehyde reduction.8,25
One potential industrial application is related to the two-step
Cetus process for production of high-purity fructose:14,26 i)
D-glucose is firstly con- verted to kDG in the presence of pyranose
2-oxi- dase and catalase (to avoid the quick oxidase inacti-
vation),27,28 at 25–30 °C and pH = 6–7, with very high conversion
and selectivity; ii) the kDG is then reduced to D-fructose by
NAD(P)H-dependent ALR at 25 °C and pH = 7, the NAD(P)+ being
in-situ or externally regenerated and re-used.22,29,30
When developing an industrial biosynthesis, the engineering aspects
related to bioreactor selec- tion, optimal operation and control,
are all based on qualitative-quantitative information on the enzyme
characteristics (stability, activity, sensitivity to oper- ating
conditions and products, deactivation rate, im- mobilization
possibilities), cofactor regeneration, and raw-material
characteristics.31–33 On the one hand, the free-enzyme (semi-)batch
operation can be preferred when enzymes exhibit high activity but
also a high deactivation rate, and the enzyme is cheap and the
product can be easily separated, or its contamination with the
enzyme is not important. However, in most cases the use of
immobilized en- zymes is more advantageous due to easy product
separation (with less allergenic enzyme impurities), less enzyme
loss, increased enzyme stability (and storage/recycling
possibility), enzyme protection against harmful environmental
stress, and better control of the process. The enzyme is
immobilized on a suitable support (powder, beads, foils, fibres,
mesoporous matrices, etc.) made from a large vari- ety of materials
(aluminium silicates, ceramics, clay, gels, charcoal, polymers,
etc.) tailored to in- crease enzyme stability with less influence
on its activity. Enzyme immobilization methods include: adsorption
on solid carriers (through hydrophobic interactions, hydrogen or
ionic bonds), entrapment (within the interstitial space of
water-insoluble polymers), encapsulation (in gels, lipids, polymers
coated with a semi-permeable membrane), cova- lent-binding (between
enzymes and the functional- ized support matrix through groups that
are not im- portant for catalytic activities of the enzyme),
cross-linking (with multifunctional cheap reagents leading to more
stable derivatives), and molecular imprinting (by applying specific
preparative strate- gies that place binding or functional groups at
de- fined positions in imprinted sites of the support).34–40 The
advantages and disadvantages of each em- ployed technique are
largely presented in the litera- ture. Modern technologies also
employ chemical modification of enzymes, or production of modified
enzymes by molecular design, prior to their immo-
bilization.1,38,41 However, enzyme immobilization is costly, and
has to be carefully engineered to over- come the significant
decrease in activity due to the
G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395 (2013)
387
matrix-enzyme interactions (changing the enzyme structure), and due
to resistance introduced by the diffusion transport through the
support. Moreover, when the enzyme deactivation rate is high
enough, the use of fixed-/fluidized-bed reactors with immo- bilized
enzymes on solid carriers becomes too cost- ly and inoperable,
requiring frequent biocatalyst regeneration/replacement.
One additional engineering aspect to be solved for biocatalytic
reactions that use an enzyme cofac- tor (e.g. NADPH or NADH in the
ALR-catalyzed reduction reactions) refers to its continuous regen-
eration (in-situ or externally). Various alternatives can be
employed: electron transfer from an elec- trode via intermediate
redox reactions (electrochem- ical route), parallel enzymatic
oxidation reactions (enzymatic routes), (photo)chemical redox reac-
tions, or regeneration using the living cell metabo- lism
(biological route), all being developed in vari- ate continuous
systems (membrane, hollow-fibre, packed-beds, or
fluidized-beds).1,22,42–45
Beside the thermal and chemical stability of the enzyme, one of the
key-points in solving the engi- neering aspects of the process
development is relat- ed to the knowledge of an adequate process
kinetic model based on a formulated reaction pathway. However,
modelling complex enzymatic processes involving a significant
number of unstable interme- diates and steps is a difficult task
because the model has to reflect the process complexity under
variate operating conditions, starting from a limited num- ber of
observed variables recorded with a limited sampling frequency, and
often with a low reproduc- ibility due to the enzyme’s high
sensitivity to the operating conditions. In spite of that,
tremendous progress has been made in developing mechanisti-
cally-based biochemical process models of various detailing degrees
(at biocatalyst, reaction, reactor, and process level),2 by using
comprehensive sys- tematic approaches and mathematical tools.
4,31,46
In particular, modelling the ALR-catalysed re- duction of aldo-keto
derivates of saccharides is a steady step due to the involved
significant number of unstable intermediates (up to 6)24 of large
mole- cules linking the substrate, the products, the enzyme and its
cofactor (usually NADPH), and difficult to be quantitatively
recorded. Various aspects of the ALR catalytic mechanism have been
studied, and several models have been proposed, with the identi- ty
of the residue donating the proton proving con- troversial.9 Recent
results suggested that h-ALR may overcome the difficulty of
“simultaneously sat- isfying the requirements of being an effective
cata- lyst and a promiscuous one by using a distal proton donor
(Asp-43–Lys-77 pair) acting through the flexible side chain of the
final proton donor (Tyr- 48)”,9 being thus capable of unspecific
accommo-
dating of different substrates. The reaction debuts with the very
fast (few seconds)24 coupling of ALR to NADPH leading to a quite
stable complex. How- ever, the substrate presence triggers
formation of successive intermediates involving a succession of
reversible ordered Bi-Bi reactions.8,13,17,19 Most of the proposed
kinetic models assume that these suc- cessive reactions quickly
reach their quasi-equilibri- um, while the conformation change
required for NADP+ release in the last step is rate-limiting for
the whole process. To overcome the large number of rate constants
of low estimability (leading to esti- mated lumps),13,24 some
attempts use reduced mod- els assuming a non-competitive substrate
/NADPH inhibition,25 or omit formation of instable enzy me- -co
factor-substrate complex (i.e. the Theorell-Chance kinetic
mechanism with the enzyme-co enzyme product dissociation being the
rate-limiting step for the overall reaction).19,47,48
The aim of this work was to study several ki- netic aspects of the
complex reaction of kDG con- version to fructose using commercial
ALR and NADPH. On the one hand, a quantitative analysis of the
process kinetics is developed based on sys- tematic batch
experiments conducted using sus- pended ALR (recombined human ALR
in E. coli) and for various enzyme/reactants initial ratios, in
order to check and complete the reaction ‘core’ mechanism proposed
in literature. The estimated model parameters based on the recorded
data (key species concentration dynamics) were compared to
literature values reported for similar ALR-catalyzed reduction
reactions. On the other hand, the model- ling analysis reveals some
quantitative aspects of practical interest, thus pointing out the
rate-limiting step in the direction of substrate reduction, the
qua- si-stability of the ALR•NADPH complex, the fast deactivation
of the enzyme, and the low level of active NADPH in the environment
during the reac- tion. The results clearly indicate the requirement
of enzyme stabilization by using a suitable immobili- zation
method, as well as the necessity of continu- ous in-situ
regeneration of NADPH cofactor.
Experimental section
Enzymes and reagents
The experiments were conducted in a thermo- statically controlled
system using commercial grade compounds from Sigma–Aldrich:
2-keto-D-glu- cose; 2,3,5-triphenyltetrazolium chloride (TTC); 6 N
NaOH solution; acetic acid; ethanol; hydrochlo- ric acid; fructose;
resorcinol; thiourea; NADPH; 0.01 mol L–1 phosphate buffer solution
of pH = 7. ALR (EC 1.1.1.21, commercial recombinant en- zyme
produced by expressing the human ALR in
388 G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395
(2013)
E. coli; enzyme activity of 0.6 U mg protein–1) was purchased from
ATGEN (product number ALR0901). The h-ALR activity was evaluated at
25 °C in 0.1 mol L–1 phosphate buffer of pH = 7 in the pres- ence
of 10 mmol L–1 DL-glyceraldehyde and 0.3 mmol L–1 NADPH as
substrates (ATGEN test conditions).
The conversion of 2-keto-D-glucose was as- sessed by applying the
same spectrometric proce- dure described by Maria et al.27 The
detection meth- od is based on a different reduction rate of
2,3,5-triphenyltetrazolium chloride in the presence of various
sugars in triphenylformazan. In the pres- ent case, the kDG reduces
TTC to a red pigment, while fructose presents no effect on the TTC.
The analysis uses 0.010 mL sample in a 4 mL test tube, by adding
0.020 mL 1 % aqueous TTC and 0.08 mL 6 N solution of NaOH. After
exactly 5 minutes, 3 mL acetic acid:ethanol (1 : 9) is added, and
the test tube content is homogenized by inversion. The absorbance
of each sample was analysed by spec- trophotometry at 480 nm and
the unchanged 2-ke- to-D-glucose content was relatively quantified
to a standard curve generated using 2-keto-D-glucose from
Sigma.
The decomposition of NADPH can be followed directly by the decrease
in absorbance at 340nm (e340 = 6.2 ± 0.3 · 103 L mol–1 cm–1).21
Enzymatic activity was confirmed by measuring the amount of enzyme
catalyzing the oxidation of 1 µmol L–1 NADPH/min. at 25 °C.
Determination of fructose concentration in samples was based on the
property of carbohydrates to form furfural in the acid environment,
which sub- sequently reacts with resorcinol to form a red com-
pound. The reaction mixture contained: 80 µL of sample, 40µL of
resorcinol reagent (1g resorcinol and 0.25g thiourea dissolved in
100 mL glacial ace- tic acid), and 0.280 µL of diluted hydrochloric
acid (five parts concentrated HCl mixed with one part distilled
water). The reaction mixture is heated in a water bath at 80 °C for
exactly 10 minutes. The tubes are then cooled by immersing them in
tap wa- ter for 5 minutes, and absorbance is read at λ = 520 nm
within 30 minutes.49 The fructose content is relatively quantified
from a standard curve generat- ed using fructose from Sigma.
Batch experiments of kDG reduction to fructose
Free enzyme experiments were carried out in a small reaction vessel
(precision Hellma cells made of Quartz SUPRASIL, of 10 mm
thickness), filled with 1.8–2.5 mL reaction liquid, and equipped
with an on-line temperature recording system. The sealed
milli-reactor (to prevent solvent vaporization) was placed in a
UV/VIS spectrophotometer Lambda 25
with a thermostatic mixing system and a PTP-6 tem- perature-control
unit of the following performances: 0–100 °C temperature range, of
0.1 °C readout res- olution and ±0.01 °C readout stability,
heating/cool- ing temperature programming rate of 10 °C min–1, 1800
rpm stirrer speed. The reaction was conducted at 25 °C and pH = 7
in a 10 mmol L–1 phosphate buffer, with various initial conditions
covering the range of [kDG] = 15–35 mmol L–1, [NADPH] = 6–35 mmol
L–1, and [ALR] = 0.0026–0.0060 U mL–1. The shaking system (a
magnetic stirrer in the cu- vette) ensured satisfactory
homogenization of the bioreactor content, while the phosphate
buffer pre- served quasi-constant pH. A slight increase in pH to
7.4 was recorded at the end of the batch due to the environmental
H+ consumption by the main reac- tion (Table 1). However, the minor
pH increase is assumed to present a negligible effect on the en-
zyme activity as long as the optimum range for the human-type ALR
covers the interval pH = 7–8.23,24
Even if the NADPH concentration declined sharply at the beginning
of the reaction, the prog- ress of the kDG reduction was
continuously moni- tored over large batch times (up to 4600
minutes) to confirm the reversible formation of the ALR•NADPH
complex maintaining a low level of NADPH in the reactor, and
characterize enzyme de- activation. Small samples taken during the
reaction were analysed separately to determine the concen- tration
of kDG (10 µL samples), fructose (80 µL samples) and the ALR
residual activity (10 µL sam- ples). Aliquoted samples in vials
were immediately stored at –70 °C for future analysis. Enzyme
assays and sample analyses were performed in duplicate, leading to
an approximate estimate of the noise lev- el for every recorded
species, that is the standard deviations of kDG = P = NADPH = 1.5
mmol L–1, and ALR = 10–4 U mL–1.
Experiments at low initial concentrations of substrate and NADPH
are not interesting from the engineering point of view due to the
obtained low conversions and reactor productivity. The recorded
dynamic evolution of the main species concentra- tions, displayed
in Figs. 1–4, was further used to estimate the rate constants of
the kinetic model.
Modelling the enzymatic process kinetics
Reaction pathway
Several studies from literature indicate that the ‘core’ mechanism
of ALR and NADPH action on aldo-keto derivates involves a
succession of several rapid reversible Bi-Bi reactions.8,13,17,19
Since the equilibrium is reached quickly, quasi-stationarity could
be assumed of the transitory complexes
G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395 (2013)
389
Ta b l e 1 – Kinetics and batch reactor model proposed for
keto-D-glucose enzymatic reduction using NADPH and suspended aldose
reductase (commercial recombinant ALR obtained by expressing human
1-316aa plasmids in E. coli; enzyme source: ATGEN, Cat. no.
ALR-0901). Notations: E = aldose reductase; A = NADPH; A+ = NADP+;
S = kDG (substrate); P = fructose (product)
Overall reactions:
ALR ( ) , 6 10 6 6 12 6(phosphate buffer)
C H O (S) NADPH (A) H C H O (P) NADP ( )PE r A+ + ++ + +
y (ALR NADPH ) NADPH ALR kd
k d y
+
ALR (E) inactive ALR (Ein)ir Rate expressions (see scheme of Fig.
5):
R
[ ] 1 [ ][ ] [ ][ ]
K [ ]
[ ] [ ][ ] [ ] 1
P
r A A S A
K K K K
, (successive Bi-Bi mechanism)
[ ][ ] [ ]
P dS dP dA
r dt dt dt
r y y dt = +
*
dt =
liquid volume = 1.8–2.5 mL 10 mmol L–1 phosphate buffer pH = 7 25
°C [kDG] = 0–35 mmol L–1
[NADPH] = 0–35 mmol L–1
initial [ALR] = 0.0026–0.0060 U mL–1
F i g . 1 – Dynamics of the observable species concentration for
keto-D-glucose enzymatic reduction using NADPH and sus- pended ALR.
Initial conditions: 35 mmol L–1 kDG, 35 mmol L–1 NADPH, 0.0057 U
mL–1 ALR, 10 mmol L–1 phosphate buffer, pH = 7; 25 °C. Model
predictions are represented by full line, and experimental values
by ‘circles’.
F i g . 2 – Dynamics of the observable species concentration for
keto-D-glucose enzymatic reduction using NADPH and sus- pended ALR.
Initial conditions: 35 mmol L–1 kDG, 35 mmol L–1 NADPH, 0.00257 U
mL–1 ALR, 10 mmol L–1 phosphate buffer, pH = 7; 25 °C. Model
predictions are represented by full con- tinuous line, and
experimental values by ‘diamonds’.
390 G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395
(2013)
formed between ALR, NADPH and substrate. Sim- plified expressions
of the overall reaction rate can be derived by including the
equilibrium constants of the intermediate steps.50 Thus, the main
reaction pathway proposed for the studied h-ALR catalyzed reduction
of kDG with NADPH, is presented in Fig. 5. The main intermediate
steps and deactiva- tion side-reactions are the following (with
notations E = ALR; A = NADPH; A+ = NADP+; S = kDG; P = fructose;
Ein = inactive form of enzyme):
i) The first very rapid reaction is the A binding to E, in large
amounts, to form a quasi-stable com- plex (E*Ay), which is inactive
for substrate binding, probably due to the transient unfavourable
configu- ration of sites. As experimentally proved by Grim- shaw et
al.24 this is a very fast binding reaction (of high dk much larger
than dk in Table 2), taking place over a few seconds, confirmed by
our experi-
mental observations. Most of the reported models in the literature
do not consider the formation of this catalytically inactive
complex, even if ”inactive” forms of ALR have been identified by
several au- thors.24 This, apparently parallel, reaction is sug-
gested by the experimental evidence in Figs. 1–4, revealing a
continuous reaction progress in terms of consumed kDG and formed
fructose in spite of the initial, very sharp decrease in [NADPH]
from 6–35 mmol L–1 to low but quasi-constant levels of 0.1–0.3 mmol
L–1. Otherwise, a monotonous [ NADPH] trajectory should be
expected, similar to the exponential-like [kDG] curve. This
experimen- tal evidence suggests that the kDG reduction does not
stop due to the NADPH sharp initial decrease, but only slows down,
while small amounts of cata- lytically active (EA) complex are
continuously formed triggered by the presence of the
substrate.
ii) In parallel, a small fraction of enzyme is rapidly binding to
NADPH by forming an active complex (EA) suitable for further
coupling the sub- strate. The reaction can be considered at
quasi-equi- librium (of /A a aK k k= constant in Table 2). As
remarked by Petrash et al.19 this enzyme activation “induces a
conformational change of enzyme E•A ↔ E’•A that involves hinge-like
movement of a surface loop so as to cover a portion of the coen-
zyme in a fashion similar to a safety belt.” The en- zyme
isomerization is not very rapid, having an av- erage equilibrium
constant of O(10–1) (Table 2).8 As further revealed by the
identified model constants, only a small fraction of the enzyme
follows this route comparatively to the formation of the inactive
(E*Ay) complex.
F i g . 3 – Dynamics of the observable species concentration for
keto-D-glucose enzymatic reduction using NADPH and sus- pended ALR.
Initial conditions: 35 mmol L–1 kDG, 6 mmol L–1 NADPH, 0.0055 U
mL–1 ALR, 10 mM phosphate buffer, pH = 7; 25 °C. Model predictions
are represented by full line, and experimental values by
‘squares’.
F i g . 4 – Dynamics of the observable species concentration for
keto-D-glucose enzymatic reduction using NADPH and sus- pended ALR.
Initial conditions: 15 mmol L–1 kDG, 35 mmol L–1 NADPH, 0.006 U
mL–1 ALR, 10 mmol L–1 phosphate buffer, pH = 7; 25 °C. Model
predictions are presented by full line, and experimental values by
‘stars.
F i g . 5 – The reaction pathway proposed for keto-D-glucose
enzymatic reduction using NADPH and suspended ALR. Nota- tions: E =
aldose reductase (ALR); A = NADPH; S = kDG (substrate); P =
fructose (product); Ein, (E*Ay) = inactive forms of the
enzyme.
G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395 (2013)
391
iii) The presence of the substrate triggers the formation of an
instable complex (EAS) which quickly ( /eq p pK k k= >> /R r
rK k k= ) leads to fructose-product formation “by transfer of the
pro-R hydride of NADPH to the re-face of the substrate carbonyl
carbon”.19 The compulsory-order mecha- nism involving the formation
of the ternary com- plex was experimentally proved by Ryle and Tip-
ton21 in the case of pyridine-3-aldehyde reduction, although the
complementary iso-Theorell-Chance mechanism cannot be totally
excluded [in which the enzyme-substrate complex is oxidized by the
elec- tron acceptor so rapidly that the ternary complex (EAS)
becomes kinetically insignificant].
iv) After the product release, a second confor- mation change is
required (E’•A+ ↔ E•A+, not ex- plicitly included in the model) in
order to release the oxidized coenzyme NADP+. Various kinetic
studies proved that this conformation change re- quired for NADP+
release represents the rate-limit- ing step of the whole process in
the direction of substrate reduction, the equilibrium
constant
/AP ap apK k k= being one-two orders of magni- tude smaller than
all other equilibrium constants from the successive reaction scheme
(Table 2).
v) Experimental observations in Figs. 1–4 re- veal a quite fast
enzyme deactivation, in parallel to other reactions. Even if the
complex (E*Ay) slow dismemberment partially compensates the active
enzyme loss (see enzyme mass balance in Table 1), the inactivation
process leads to maintaining a low enzyme level during most of the
reaction.
Globally, the overall reduction reaction dis- played in Table 1 is
accompanied by a side-re- versible binding of ALR to the co-enzyme
NADPH to form an inactive complex, and by the enzyme deactivation
reaction. The present study will check the validity of the
successive reversible Bi-Bi reaction scheme in the case of kDG
substrate, the characteristics of the side-reactions, the signifi-
cance of the estimated rate constants, and will use the model
predictions to derive practical conclu- sions of interest for
further improvement of the pro- cess.
Rate constant identification and results discussion
Based on the proposed reaction pathway in Fig. 4, a hyperbolic
expression of the overall reaction rate was derived (Table 1), by
assuming rapid equi-
Ta b l e 2 – Identified kinetic parameters, significance tests, and
literature data for keto-D-glucose enzymatic reduction using NADPH
and suspended aldose reductase (kinetic parameters for 25 °C, pH =
7; commercial recombinant ALR from ATGEN, Cat. no. ALR-0901). The
t-tests computed with minimum relative noise of = 0.024 (see
Appendix of Treitz et al.51 for de- tails)
Parameter Estimate (± 95 % CI)(a) t-test(a) Ordered
/ 2 j (b) Reported value
pk , mM min–1 (U/mL) –1 (3.90 ± 1.20) · 106
(289–1560 min–1) 6.3 (√) 1 11–36 (min–1) (substrate of
glycolaldehyde,17 or glyceraldehydes8; animal ALR) 9300 min–1 (for
xylose reductase)16
AK , mmol L–1 50.58 ± 23.85 4.1 (√) 1 10–4 – 2740 (various
substrates and ALR sources) 23,24,52
RK , mmol L–1 1.15 ± 0.21 10.9 (√) 1 0.2–150 (various
substrates)25
1.06 (xylose substrate; human ALR)24
eqK , mmol L–1 1637 ± 417 7.7 (√) 1.6 446–528 (xylose
reductase)16
200 (xylose substrate; human ALR)24
APK , mmol L–1 0.99 ± 0.40 4.8 (√) 4.8 1.9 · 10–3 – 8.3 · 10–3
(glyceraldehydes)8
3 · 10–3 (xylose substrate; human ALR)24
dk , mM–1 min–1 (2.66 ± 0.14) · 106 37.7 (√) 9.7 7.2 · 106 (human
ALR)24
dk , min–1 672 ± 35 37.7 (√) 1.6 · 105 104 (human ALR)24
y , mM (U/mL)–1 (1.78 ± 0.01) · 104 2219 (√) 1.1 · 109 –
ik , min–1 (7.01 ± 0.01) · 10–2 8162 (√) 3.5 · 1012 –
ys (c) , (-) 1.04 remark:(d) adequacy χ2 – test passed
(a) a parameter is significant for t-test > t(Nm-p;0.975) = 1.98
(symbol ”√” for passed test), where N = total number of
experimental points (39) over four data sets; m = number of
observed variables (4); p = number of model parameters (9); 95 % CI
= the 95 % confidence interval of the estimate.3
(b) ridge selection test of Maria and Rippin53 is passed when / 2 j
> 1.3,51 Values of / 2
j ≈ 1 correspond to highly intercorrelated parameters, which are
difficult to estimate separately ( j = eigenvalues of the inverse
of the modified parameter covariance matrix). (c) relative standard
error deviation of the model (related to the noise error) was
computed with Eq. (1) formula. (d) model is adequate, the following
test being passed: χ2 = 45.6 < χ2(Nm-p; 95 %) = 176.3
(√).3
392 G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395
(2013)
libriums for all elementary steps of the main path, and by
eliminating the unobservable intermediate species from the rate
equation (see e.g. Segel50 for details on such a general rule for
writing equations for rapid equilibrium systems). The species mass
balance also includes the side reactions of revers- ible enzyme
binding to NADPH (of dk and dk rate constants), and of enzyme
irreversible deactiva- tion. In order not to complicate the kinetic
model, a first-order ALR inactivation model was adopted (of
ik deactivation constant). An ideal batch reactor model was adopted
(iso-
thermal, perfectly mixed), in order to simulate the batch
experiments, by including the mass balance equations of Table 1.
The rate constants were fitted by adjusting the model predictions
to match the experimental concentration-time profiles of kDG,
fructose, NADPH, and active ALR. The used data sets cover four
batch tests by using variate initial conditions in the ratios of
[kDG] / [NADPH] / [ALR] = 35 / 35 / 0.0057, 35 / 35 / 0.00257, 35 /
6 / 0.0055, and 15 / 35 / 0.006 (mmol L–1/ mmol L–1/ U mL–1)
respectively. A weighted least square crite- rion was used as
statistical estimator of the rate con- stant vector k, by
minimizing the relative error vari- ance of the model, that
is:3
k= arg Min ( 2 ys );
2 ys = (
1
c c ) / mN p , (1)
j = kDG, NADPH, fructose, ALR
where: N = the number of experimental points (i.e. 39 reaction
times); m = the number of observed variables (4 here); p = the
number of model param- eters (9 here), ‘^’ = estimated values. The
adaptive random optimization algorithm MMA/MMAMI of Maria,54
implemented in MatlabTM, was used as an effective solver. The
multimodal search was started from an initial guess of the kinetic
parameters ran- domly generated within the reported variation do-
main of Table 2 (last column) (except the ik deacti- vation
constant, which was approximated from the [ALR] experimental
plots).
The estimated model parameters for 25 °C are presented in Table 2
together with the associated 95 % confidence interval, and
statistical t-test of estimate quality. Model predictions displayed
in Figs. 1–4 for all data sets (solid lines) are in good agreement
with the experimental data (points). The model is globally
adequate, while the average rela- tive error of the model ys = 1.04
is acceptable, being comparable to the experimental minimum rel-
ative noise. The analysis of the estimated rate con- stants (Table
1) and model predictions (Figs. 1–4) leads to several
conclusions:
i) in spite of slight overparameterization (i.e. 9 parameters vs. 4
observed variables recorded over 39 runs), the proposed kinetic
model is robust and offers adequate predictions irrespective of the
cho- sen initial concentrations of species over the in- vestigated
operating domain of [kDG] = 0–35 mmol L–1, [NADPH] = 0–35 mmol L–1,
initial [ALR] = 0.0026–0.0060 U mL–1. Such a conclu- sion could
support the adoption of the above-pre- sented ‘core’ mechanism from
literature derived for similar reduction processes, including
h-ALR24 or animal-ALR17 catalysed reactions.
ii) the statistical tests were roughly passed, i.e. an acceptable
model global adequacy (χ2 test was passed, displaying a smaller
value than the theoret- ical 95 % χ2-quantile; see Table 2-footnote
d), and fairly significant rate constants (i.e. t-tests higher than
the relevant quantile value of Table 2-footnote a, and most of /
2
j test values higher than 1, see Table 2-footnote b). The 95 %
confidence intervals of the estimated constants are satisfactorily
small, the larger ones corresponding to estimated parame- ters
presenting smaller t-tests ( AK , APK , and pk ). Besides, equal
t-tests of dk and dk constants indi- cate their high
inter-correlation, leading to the im- possibility of their separate
estimation without addi- tional information. According to the more
sensitive
/ 2 j significance test of Maria and Rippin53,
there are three constants of low estimability, corre- sponding to
AK , APK , and one of the dk and dk constants. Such low
estimability for some rate con- stants of the hyperbolic rate
expression models is a common subject in literature when structured
infor- mation on intermediate dynamics is lacking, some parameters
presenting inter-correlation coefficients higher than 0.95–0.99.
Consequently, their separate estimation with precision is not
possible as long as no experimental measurements concerning the
dynamics of instable intermediate species (EA), (EAS), (EA+) are
available.
iii) most of the estimated rate constants present close values or
fall within the range of variation of the corresponding rate
constants reported in the lit- erature for similar enzymatic
reduction processes, even if various sources of ALR (including
h-ALR) and aldo-keto substrates have been used; such an observation
supports the model structure choice.
iv) the high value of eqK indicates a quick electron transfer in
the (EAS) complex leading to fructose formation. It is also
confirmed that the NADP+ release from the (EA+) complex represents
the rate-limiting step, the estimated APK being smaller than the
other equilibrium constants of the reaction chain. However, the
estimated small equi- librium constant RK of Table 2 reveal that
the trig-
G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395 (2013)
393
gering step (EA) + S (EAS) is also a slow step in the chain.
v) another model confirmation is related to the fair reproduction
of the experimental evidence of a very sharp initial decline in
[NADPH] from the ini- tial 6–35 mmol L–1 to low but quasi-constant
levels of 0.1–0.3 mmol L–1. In spite of this low [NADPH] level over
the whole reaction domain (thousands of minutes), the kDG reduction
does not stop but it oc- curs quantitatively due to the continuous
decompo- sition of the (E*Ay) inactive complex triggered by enzyme
and co-enzyme consumption. In the ab- sence of such a (co-)enzyme
‘reservoir’, a monoto- nous [NADPH] trajectory should be expected,
sim- ilar to the exponential-like [kDG] decreasing curve.
vi) the experimental sharp decline of the initial [NADPH] over a
few minutes is fully confirmed by the reported decline time (of a
few seconds) mea- sured by Grimshaw et al.24 when reducing D-xylose
using h-ALR. This evidence translates into an esti- mated high dk
constant, of the same order of mag- nitude as those reported for
the h-ALR coupling to NADPH.24 Even less favoured, the continuous
slow transformation of the inactive E*A complex into an active (EA)
complex (in our model via free enzyme and NADPH release) leads to
the continuous avail- ability of these species during the reaction,
even if the quick NADPH consumption and ALR inactiva- tion maintain
their low level (see Figs. 1–4). The stoichiometric coefficient y ≈
17.8 milli-moles NADPH / U ALR (Table 2) indicates very high af-
finity of enzyme to NADPH, the inactive (E*A) complex lasting
during the entire reduction process.
vii) the irreversible h-ALR enzyme inactivation oc- curs quite
rapidly (ca. 10 min half-life according to the estimated ik value)
triggering the continuous release of active enzyme from its complex
with the cofactor.
Several inhibition terms of the reduction rate have been neglected
from the rate expression, according to the experimental observation
of Leit- ner et al.,14 i.e. the fructose low inhibition until 500
mmol L–1 concentration, and the negligible in- hibition with the
kDG substrate until 100 mmol L–1 levels (i.e. [S][A] << RK AK
in the rate Pr expres- sion of Table 1). The continuous progress of
the kDG reduction in spite of a low NADPH level con- firms the
Leitner et al.14 conclusion that the reverse reaction can be
neglected.
Conclusions
Derivation of an adequate and reliable kinetic model for a complex
enzymatic process is a diffi- cult task, requiring steady
experimental efforts to
obtain sufficient information on the process dynam- ics and its
mechanism, and also extensive computa- tional efforts to derive a
comprehensible robust model with interpretable parameters. Such a
model can be further valorised in developing engineering
calculations, as long as simple separate observa- tions cannot give
the whole picture on the process characteristics, while its
parameters do not vary with the reaction initial conditions.
In spite of slight overparameterization (i.e. 9 parameters vs. 4
observed variables recorded over 39 runs), leading to a lower
estimability of two- three intercorrelated rate constants, the
derived ki- netic model for kDG reduction to fructose in the
presence of ALR and NADPH presents fair adequa- cy, with parameter
values comparable with those reported for similar systems. The
confirmed ‘core’ mechanism employed in literature for describing
various reactions catalyzed by ALR, h-ALR, and al- do-keto
reductases, is also proved applicable to the studied system, being
of satisfactory quality, robust, and with rate constants
independent of the species initial concentrations but only on the
reaction con- ditions.
The derived kinetic model reveals some inter- esting conclusions.
The very high affinity of ALR for NADPH leads to the very fast and
reversible formation of a complex ALR•NADPH of different forms
(confirmed by literature data); only a small fraction of this
complex is “active” for bonding the substrate, then leading to its
reduction to fructose by an internal electron transfer in the
ALR•NAD- PH•kDG complex. Several conformational re-ar- rangements
of the enzymes occur during the succes- sive Bi-Bi reaction steps,
the slowest step confirmed being the E’•A+ ↔ E•A+ enzyme
isomerization in order to release the NADP+. Other inhibitory ef-
fects induced by the substrate or products are insig- nificant
within the checked experimental range of [kDG] = 0–35 mmol L–1,
[NADPH] = 0–35 mmol L–1, initial [ALR] = 0.0026–0.0060 U
mL–1.
The fast deactivation of the enzyme indicates a low level of active
ALR during the reaction in spite of the slow decomposition of the
quasi-stable (E*Ay) complex. Consequently, the enzyme stabilization
by immobilization appears to be crucial for further pro- cess
development. On the other hand, the low level of active NADPH in
the environment due to its very high affinity to the ALR, clearly
indicates the re- quirement for a continuous in-situ regeneration
of NADPH by using a parallel redox reaction.
The kinetic model parameters and predictions can be useful for
further process development, while its structure can be translated
easily to sys- tems employing stabilized ALR forms. The model form
can also be useful for conducting investiga- tions into the
possibility of immobilizing ALR on a
394 G. MARIA and M. D. ENE, Modelling Enzymatic Reduction of
2-keto-D-glucose…, Chem. Biochem. Eng. Q., 27 (4) 385–395
(2013)
suitable support, or for predicting the process dy- namics when
performing in-situ regeneration of the cofactor by means of a
suitable redox reaction, thus allowing further process
optimization.
ACKNOWLEDGMENTS
The second author is grateful to the Biotehnos Co. (Otopeni,
Romania) for the experimental facili- ties offered with
generosity.
S y m b o l s
jc – species j concentration, mol L–1
jk – rate constants (in terms of mol L–1, s, U L–1 units) jK –
equilibrium constants, mol L–1
m – number of observed species N – total number of experimental
points over all data
sets (recording times) p – number of model independent
parameters
jr – reaction rates (mol L–1 s–1, U L–1 s–1) ys , 2
ys – standard error deviation of the model, or its variance (in
relative terms, Eq. 1)
t – time (s), or statistical Student test y – stoichiometric
coefficient, mol U–1
G r e e k s
λ – eigenvalues of the inverse of the modified pa- rameter
covariance matrix3
σ – measurement error standard deviation, mol L–1, U L–1
I n d e x
t – total
S u p e r s c i p t s
^ – estimated
A b b r e v i a t i o n s
A – NADPH A+ – NADP+
(h–)ALR – (human origin–) aldose reductases E – aldose reductases
kDG – 2–keto–D–glucose NAD(P)H – Nicotinamide adenine
dinucleotide
(phosphate) reduced form P – fructose S – substrate (kDG here) TTC
– 2,3,5–triphenyltetrazolium chloride
2 – Euclidean norm
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